C₁₆²×C₁₇ #16864795

order	4352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 393216
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

C₁₆²×C₁₇

166 conjugacy classes of subgroups.

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)

4352 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 39);